slope is the rise (vertical)change divided by the run (horizontal) change.
For 2 points it's : (y2-y1) / (x2-x1)
For y = mx +b, it is the value of m in this pattern
From calculus it is the slope of the line that is tangent to the curve and this can be found from the derivative of the function: dy/dx = slope of the f(x).